Sampling frequency discrete form

Infrared emission spectroscopy forms a valuable technique that can be plied in situ during the heat treatment. The technique of measurement of discrete vibrational frequencies emitted by thermally excited molecules, known as Fourier transform infrared emission spectroscopy (FTTR ES, or shortly lES) has not been widely used for the study of materials. The major advantages of lES are that the samples are analyzed in situ at increasing temperatures and lES requires no sample treatment other than that the sample should be of submicron particle size. Further, the technique removes the difficulties of heating tiie sample to temperatures where reactions take place with subsequent quenching prior to the measurement, because lES measures the process as it is actually taking place. 

Note that real instruments do not sample continuously but in discrete, equally spaced intervals. The discrete Fourier transformation is similar in form to equation (10.3). Note also that the discrete Fourier transformation converts a series of complex time-domain data into another series of complex frequency-domain data. Even a time-domain signal containing... 

Equations [18] and [20] form a discrete Fourier transform pair that relate the discrete sample space with the frequency space. 

Because our h are discrete sampled values, they will be represented by the integral of coefficients H(f) times sinusoids of varying frequency, provided that the coefficients are appropriately selected. For this case we will work with a normalized frequency /. Normally, these equations are written with the symbol/ (no prime), but we want to make it clear that our/ is a normalized variable - the ratio of two real frequencies - so it has no units. The sinusoids for all of the other cases included an argument of the form/) - frequency times time. This one does not - because the frequency is dimensionless. 

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